Limited-angle frequency-distance resolution recovery in nuclear medicine imaging

ABSTRACT

A nuclear camera ( 10 ) includes a plurality of detector heads ( 12 ) which have collimators ( 14 ) for fixing the trajectory along which radiation is receivable. A rotating gantry ( 22 ) rotates the detector heads around the subject collecting less than 360° of data, e.g., 204° of data. A zero-filling processor ( 50 ) generates zero-filled projection views such that the actually collected projection views and the zero-filled projection views span 360°. A smoothing processor ( 56 ) smooths an interface between the zero-filled and actually collected projection views. The zero-tilled and smoothed views are Fourier transformed ( 60 ) into frequency space, filtered with a stationary deconvolution function ( 62 ), and Fourier transformed ( 64 ) back into real space. The resolution recovered projection data sets in real space are reconstructed by a reconstruction processor ( 68 ) into a three-dimensional image representation for storage in an image memory ( 70 ).

BACKGROUND OF THE INVENTION

[0001] The present invention relates to the diagnostic imaging art. Itfinds particular application in conjunction with nuclear single photonemission computed tomography (SPECT) medical imaging and will bedescribed with particular reference thereto. However, the invention willalso find application in conjunction with other types of non-invasivediagnostic imaging.

[0002] Heretofore, diagnostic images have been generated from single andmultiple-head nuclear cameras. Typically, a patient positioned in anexamination region is injected with a radio pharmaceutical. Heads of thenuclear camera are positioned closely adjacent to the patient to monitorthe radio pharmaceutical. Typically, the heads are stepped in incrementsof a few degrees around the patient until 360° of data have beenacquired. That is, projection data along directions spanning 360° arecollected. With multiple-head systems, projections along each directionneed only be collected with one of the heads and be assembled into acomplete data set.

[0003] Each detector head carries a collimator which defines a pathalong which it can receive radiation. However, due to the finite lengthand dimensions of the collimator, each incremental area of the detectorhead actually views an expanding cone. Thus, with increasing depth intothe patient away from the detector head, the region from which a sensedradiation event originated expands. This creates depth-dependentblurring and uncertainty in the resultant image data. This error is anon-stationary convolution which is difficult to deconvolve. However,when the patient is viewed over a full 360°, the angular data sets areperiodic in 2π radians. By transforming the full data sets into thefrequency domain with a Fourier transform fit to the sampling intervals,the non-stationary deconvolution is reduced to a stationarydeconvolution problem, particularly for high frequencies.

[0004] Although these prior art resolution recovery techniques work wellon full data sets, cardiac imaging is typically done using an incompletedata set. More specifically, in a three-head camera system where onlytwo heads collect the emission data while the third head is used tocollect transmission data, the gantry is rotated by about 102° togenerate the equivalent of only about 204° of emission data. The priorart resolution recovery techniques do not work on partial data setswhose data is not periodic in 2π radians.

[0005] The present invention contemplates a new and improved method andapparatus which overcomes the above-referenced problems and others.

SUMMARY OF THE INVENTION

[0006] In accordance with one aspect of the present invention, a methodof diagnostic imaging is disclosed. A plurality of projection data setsare collected at each of a plurality of angles around a subject. Theprojection images are collected over less than 360°. A resolutionrecovery process is performed on the projection data sets. Theresolution recovered projection data sets are reconstructed into animage representation.

[0007] In accordance with another aspect of the present invention, amethod of diagnostic imaging is disclosed. A gantry moves a detectorhead in a continuous angular orbit about a subject in an examinationregion. Data is collected during the continuous orbit and sorted into aplurality of projection data sets corresponding to each of a pluralityof angular increments around a subject. A resolution recovery process isperformed on the projection data sets. The resolution recoveredprojection data sets are reconstructed into an image representation.

[0008] In accordance with yet another aspect of the present invention, adiagnostic imaging apparatus is disclosed. At least one detector headdetects incident radiation. A collimator mounted to the detector headlimits trajectories along which radiation is receivable by the head. Amovable gantry moves the detector head around a subject in anexamination region. A data acquisition system acquires projection datasets from the detector head at angular increments spanning less than360°. A zero-filling processor generates zero-filled data sets betweenthe actually collected projection data sets, to create 360° of datasets. A smoothing processor smooths interfaces between the actuallycollected and zero-filled data sets. A resolution recovery processoroperates on the smoothed data sets. A reconstruction processorreconstructs the resolution recovered data sets into a three-dimensionalimage representation. An image memory stores the three-dimensional imagerepresentation.

[0009] One advantage of the present invention is that it accuratelyrestores limited-angle data sets.

[0010] Another advantage of the present invention is that it restorescontinuously scanned data sets.

[0011] Another advantage of the present invention is that it processesimage data in a clinically feasible time.

[0012] Still further advantages and benefits of the present inventionwill become apparent to those of ordinary skill in the art upon readingand understanding the following detailed description of the preferredembodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The invention may take form in various components andarrangements of components, and in various steps and arrangements ofsteps. The drawings are only for purposes of illustrating preferredembodiments and are not to be construed as limiting the invention.

[0014]FIG. 1 is a diagrammatic illustration of a nuclear medicineimaging system in accordance with the present invention;

[0015]FIG. 2 is a diagrammatic illustration of the formation of themodified data set which is periodic in 2π radians, based on thenon-periodic limited-angle data set;

[0016]FIG. 3 shows the coordinate system used in data acquisition andimage reconstruction.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0017] With reference to FIG. 1, a nuclear camera system 10 includes aplurality of detector heads 12, in the preferred embodiment threedetector heads 12 ₁, 12 ₂, and 12 ₃. Two of the three heads aretypically used to obtain emission data, while the third head is used toobtain transmission data. Of course, other numbers of detector heads canalso be utilized. Each of the detector heads includes a collimator 14 ₁,14 ₂, and 14 ₃. In the preferred embodiment, the collimators collimateincoming radiation from a subject 16 to parallel rays. However, becausethe collimators have finite size, each collimator permits rays which liealong a corresponding cone to pass to the detector head. The coneexpands with depth into the patient from the detector head.

[0018] Each of the detector heads includes a reconstruction system 20 ₁,20 ₂, and 20 ₃ which determines the coordinates on a face of thedetector head in the longitudinal or z-direction of the patient and thetransverse direction across the detector head. With the detector head ina single orientation, scintillation events are collected for apreselected period of time to generate a projection imagerepresentation. After the preselected data acquisition duration, arotating gantry 22 rotates all three detector heads concurrently a shortangular distance, e.g., 3°. In the new location, each of the detectorheads collects another projection image. An angular orientation monitor24 determines the angular orientation of each of the heads at eachangular data collection position.

[0019] A data acquisition system 30 receives each of the projectionimages and an indication of the angle along which it had been taken.This data is stored in a three-dimensional memory 32 in longitudinal(z), lateral (s), and angular (ø) coordinates.

[0020] With continuing reference to FIG. 1 and further reference to FIG.2, the rotating gantry 22 rotates the detector heads over 102° forcardiac imaging. Rotation over 102° generates the equivalent of about204° of emission data 110 collected by two camera heads. Each data setis collected at equal angular increments, e.g., 3°. FIG. 2 shows anincomplete data set with no data collected between 204° and 360° in theangular dimension. Simultaneously, the third camera collectstransmission data over the 102° gantry rotation.

[0021] With continuing reference to FIG. 2 and reference again to FIG.1, a resolution recovery system 42 includes an angular displacementdimension resolution recovery system and optionally includes resolutionenhancement sub-system 46 for the axial dimension. The resolutionrecovery system in the angular direction (ø) has a zero-fillingprocessor 50 which creates zero magnitude projection data sets 112 ateach of the 3° intervals between 204° and 360°. In this manner, afunction which is periodic in 2π radians is created. In order to preventGibbs' ringing, the sudden discontinuities at each end of the actuallycollected data 110 between the actually collected and zero-filled data112 are smoothed by a smoothing processor 56. In the preferredembodiment, the magnitude of the end points are each cut in halfproducing modified data points 114 and 116. Optionally, other smoothingfunctions which span several points at each end are also contemplated.

[0022] A Fourier transform processor 60 transforms the data into thefrequency domain. The Fourier transform is selected to match all of thesampling points including the zero-filled points in the angulardimension. A stationary deconvolution processor 62 operates on thefrequency-spaced data. In frequency space, the deconvolution problemreduces to a stationary deconvolution problem, particularly for highfrequencies. Because high frequencies correspond to fine detail, it isthe high frequencies which correspond to the resolution to be optimized.The additional deconvolution 46 may optionally also be performed toimprove image resolution in the z-direction. After the data has beendeconvolved, an inverse Fourier transform processor 64 transforms thedata from the frequency domain back into real space. Optionally, athree-dimensional memory 66 stores the resolution recovered sets ofprojection data. A reconstruction processor 68 reconstructs theprojection data sets, using filtered back-projection, iterativereconstruction, or other techniques which are well-known in the art, andstores the resultant image in a three-dimensional image memory 70. Avideo processor 72 withdraws selected portions of the reconstructedimage and converts it to appropriate format for display on ahuman-readable monitor 74, such as a video monitor, CCD display, activematrix, or the like. The video processor may withdraw selected slices,three-dimensional renderings, projection views, or the like.

[0023] In one alternate embodiment, the movable gantry 22 rotates thedetector heads continuously. Although the detector heads rotatecontinuously, the data acquisition system 30 bins the collected datainto regular angular intervals, e.g., 3°. Because the data is collectedover 3° of rotation, there is an additional blurring component. Asdescribed in greater detail below, the stationary deconvolutionprocessor 62 deconvolves the Fourier space data with respect to theblurring caused by the continuous motion and treats data collected overa few degrees as if it were all collected at precisely the same angle.

[0024] With reference to FIG. 3, and looking now to details of theresolution recovery system, the working principles are explained intwo-dimensions and circular orbits, but the generalization tothree-dimensions is straightforward and generalization to non-circularorbits is known to those conversed in the art. The third dimension, z,is perpendicular to the plane defined by the x-y axes. The scannercollects data in coordinates (s, ø) which are the sinogram coordinatesof the Radon transform coordinates. The unblurred or undegraded Radontransform of the object o is the line integral along t, the axisperpendicular to s. In a nuclear medicine tomographic device, the objecto is blurred by a point response function g. This process is modeled bya convolution in s. The amount of blurring depends on the depth t.Hence, the blurring function is a non-stationary convolution of o withg. The result is the blurred Radon transform p. For limited-angletomography, this operation of the scanner is represented by:$\begin{matrix}{{{p\left( {s,\varphi} \right)} = {\int_{- \infty}^{\infty}{\int_{- \infty}^{\infty}{{g\left( {{s - s^{\prime}},t} \right)}{o\left( {{s^{\prime}\theta} + {t\quad \theta^{\bot}}} \right)}{s^{\prime}}{t}}}}},} & (1)\end{matrix}$

[0025] where θ and θ^(⊥) are two-dimensional unit vectors aligned withthe (s,t) axes:

θ:[cos φ, sin φ] and θ^(⊥):[−sin φ, cos φ]  (2).

[0026] A point source located at x in the object will have thepoint-source projection: $\begin{matrix}{{P_{\delta} = {{\int_{- \infty}^{\infty}{\int_{- \infty}^{\infty}{{g\left( {{s - s^{\prime}},t} \right)}{J}{\delta \left( {{s^{\prime} - {x \cdot \theta}},{t - {x \cdot \theta^{\bot}}}} \right)}{s^{\prime}}{t}}}} = {g\left( {{s - {x \cdot \theta}},{x \cdot \theta^{\bot}}} \right)}}},} & (3)\end{matrix}$

[0027] where |J| is the Jacobian of the change of coordinates from (x,y)to (s,t) and is equal to one because it is a rotation. Thetwo-dimensional Fourier transform of Equation (3) gives: $\begin{matrix}\begin{matrix}{{{\hat{p}}_{\delta}\left( {\omega,n} \right)} = {\int_{0}^{2\pi}{^{{- }\quad n\quad \varphi}{\int_{- \infty}^{\infty}{^{{- {\omega}}\quad s}{g\left( {{s - {x \cdot \theta}},{x \cdot \theta^{\bot}}} \right)}{s}{\varphi}}}}}} \\{= {{\int_{0}^{2\pi}{^{{- }\quad n\quad \varphi}^{{- {\omega}}\quad {x \cdot \theta}}{\hat{g}\left( {\omega,{x \cdot \theta^{\bot}}} \right)}{\varphi}}} \approx {{\hat{g}\left( {\omega,{{x \cdot \theta^{\bot}} = \frac{n}{\omega}}} \right)}.}}}\end{matrix} & (4)\end{matrix}$

[0028] The ø-integral is evaluated using the principle of stationaryphase, an approximation process familiar to those knowledgeable in theart, which asymptotically converges to the exact value of the{circumflex over (p)}_(δ) integral at high frequencies. In Equation (4),it will be noted that the solution does not depend on the location ofthe point source. Hence, it can be applied to any point source or aweighted collection of point sources.

[0029] Furthermore, if the scanning arc is limited to something lessthan 360° or 2π radians, the basic result of stationary phase, that thedistance t is given by: $\begin{matrix}{t = {{x \cdot \theta^{\bot}} = \frac{n}{\omega}}} & (5)\end{matrix}$

[0030] is unchanged, because every distance is represented in eachplanar projection image. This enables the limits of integration inEquation (4) to be replaced with an arc or a series of disjoint arcs andEquation (5) still holds to good approximation.

[0031] In operation, the digitized three-dimensional data setp(s_(j),z_(k),ø_(m)) is collected. The digitization assumes equalincrements in each coordinate sample space. For example, the angularincrement m is taken at intervals ø_(m)=2πm/N radians, where N is aninteger.

[0032] The depth dependent, point response function g(s,z,t) isobtained. When the scan is over a limited angle arc described by theinterval [ø_(u),ø_(v)] a digital input data set is formed according tothe following process: $\begin{matrix}{{p_{in}\left( {s_{j},z_{k},\varphi_{w}} \right)} = {\begin{matrix}{{0,{{{for}\quad 0} \leq W < {\min \quad \left( {u,v} \right)}}}} \\{{{\frac{1}{2}{p\left( {s_{j},z_{k},\varphi_{u}} \right)}},{{{for}\quad W} = u}}} \\{{{{p\left( {s_{j},z_{k},\varphi_{W}} \right)}\quad {for}\quad u} < W < v}} \\{{{\frac{1}{2}{p\left( {s_{j},z_{k},\varphi_{v}} \right)}},{{{for}\quad W} = v}}} \\{{0,{{{for}\quad \max \quad \left( {u,v} \right)} < W < N}}}\end{matrix}.}} & (6)\end{matrix}$

[0033] The endpoint projection frames are multiplied by one-half toprevent excessive ringing or Gibbs' phenomena. Other smoothing functionsfor smoothing the sudden data discontinuity are also contemplated. TheFourier transform with respect to angle is selected to have dimension N,no more and no less, to preserve the cyclic nature of the data. Thethree-dimensional Fourier transform applied by the Fourier transformprocessor 60 of the modified projection data P_(in) is denoted by:

{circumflex over (p)}_(in) (ω_(s),ω_(z),n)   (7).

[0034] The filter function: $\begin{matrix}{\hat{g}\left( {\omega_{s},\omega_{z},\frac{n}{\omega_{s}}} \right)} & (8)\end{matrix}$

[0035] is defined The filter function is used in a regularized inversefilter such as a noise reduction filter or a Metz filter to perform thestationary deconvolution 62. The inverse Fourier transform processor 64takes the inverse Fourier transform of the filtered image to obtainprojection data that possesses improved resolution.

[0036] In the continuous scanning embodiment, the camera moves accordingto a preprogrammed orbit. In the preferred embodiment, the three headsmove simultaneously in a complex patient dependent orbit. Continuousmotion is advantageous for reducing motion complexity. However,continuous scanning degrades resolution. Preferably, the stationarydeconvolution module includes a component to compensate for thisdegraded resolution.

[0037] Continuous scan projection data p_(c) is related to thestep-and-shoot projection data p by: $\begin{matrix}{{p_{c}\left( {s,z,\varphi} \right)} = {\frac{1}{\Delta \quad \varphi}{\int_{{- \Delta}\quad {\varphi/2}}^{\Delta \quad {\varphi/2}}{{p\left( {s,z,\varphi^{\prime}} \right)}{{\varphi^{\prime}}.}}}}} & (9)\end{matrix}$

[0038] The Fourier transform relationship is: $\begin{matrix}{{{{\hat{p}}_{c}\left( {\omega_{s},\omega_{z},n} \right)} = {{\hat{p}\left( {\omega_{s},\omega_{z},n} \right)}\frac{\sin \left( {n\quad {{\Delta\varphi}/2}} \right)}{n\quad {{\Delta\varphi}/2}}}},{{{- \frac{N}{2}} + 1} \leq n \leq {\frac{N}{2}.}}} & (10)\end{matrix}$

[0039] These relationships hold true for non-circular and limited-angleorbits as well. The filter function for continuous sampling ĝ_(c), ismodified to include the weighted sine function from Equation (10):$\begin{matrix}{{{\hat{g}}_{c}\left( {\omega_{s},\omega_{z},\frac{n}{\omega_{s}}} \right)} = {\frac{\sin \left( {n\quad {{\Delta\varphi}/2}} \right)}{n\quad {{\Delta\varphi}/2}}{{\hat{g}\left( {\omega_{s},\omega_{z},\frac{n}{\omega_{s}}} \right)}.}}} & (11)\end{matrix}$

[0040] In accordance with another alternate embodiment, in thestep-and-shoot imaging mode, the actually collected data integrals maybe disjoint. It is not necessary for all of the angular views to beadjacent as in the example above.

[0041] The invention has been described with reference to the preferredembodiments. Obviously, modifications and alterations will occur toothers upon reading and understanding the preceding detaileddescription. It is intended that the invention be construed as includingall such modifications and alterations insofar as they come within thescope of the appended claims or the equivalents thereof.

Having thus described the preferred embodiments, the invention is nowclaimed to be:
 1. A method of diagnostic imaging comprising: collectinga plurality of projection data sets at each of a plurality of anglesaround a subject, the projection images being collected over less than360°; performing a resolution recovery process on the projection datasets; and reconstructing the resolution recovered projection data setsinto an image representation.
 2. The method as set forth in claim 1wherein the projection data sets span less than 360°.
 3. The method asset forth in claim 1 wherein the projection data sets are collectedspanning 204°.
 4. The method as set forth in claim 1 wherein theresolution recovery step is performed in at least an angular rotationdimension, the resolution recovery step including: zero-fillingprojection image data sets in the angular rotation direction, such thatthe zero-filled and actually collected projection data sets togetherspan 360° at regular angular increments.
 5. The method as set forth inclaim 4, further including: smoothing an interface between the actuallycollected and zero-filled data sets.
 6. The method as set forth in claim5 further including: transforming the smoothed data sets into frequencyspace; stationarily deconvolving the frequency space data sets with aresolution recovery filter function; and transforming the stationarilydeconvolved data sets from frequency space to image space.
 7. The methodas set forth in claim 6 further including: rotating detector headscontinuously around the subject; binning projection data collected overpreselected angular increments into the projection data sets; and in thedeconvolving step, deconvolving the frequency space data sets with:$\frac{\sin \left( {n\quad {{\Delta\varphi}/2}} \right)}{n\quad {{\Delta\varphi}/2}}{\hat{g}\left( {\omega_{s},\omega_{z},\frac{n}{\omega_{s}}} \right)}$

where Δø is the angular increment corresponding to each data set, andĝ(ω_(s), ω_(z),n/ω_(s)) is the resolution recovery filter function. 8.The method as set forth in claim 5 wherein the smoothing step includes:reducing an amplitude of at least one actually collected projection dataset adjacent each zero-filled data set.
 9. The method as set forth inclaim 8 wherein the reduction in amplitude is one-half for each value ofthe original actually collected projection data set adjacent eachzero-filled data set.
 10. The method as set forth in claim 8 wherein theactually collected data is disjoint with at least four interfacesbetween the actually collected and zero-filled data sets.
 11. The methodas set forth in claim 5 wherein the step of transforming into frequencyspace includes: operating with a Fourier transform which is matched to atotal of the actually collected and zero-filled data sets.
 12. A methodof diagnostic imaging comprising: continuous movement of a gantry whichmoves a detector head in a continuous angular orbit about a subject inan examination region; collecting data during the continuous orbit andsorting the data into a plurality of projection data sets correspondingto each of a plurality of angular increments around a subject;performing a resolution recovery process on the projection data sets;and reconstructing the resolution recovered projection data sets into animage representation.
 13. The method of claim 12 wherein the smallangular increments are spaced by less than 7°.
 14. The method of claim12 wherein the angular increments are spaced by 3°.
 15. The method ofclaim 12 wherein the resolution recovery process includes correcting forblurring due to the continuous scanning.
 16. The method of claim 15wherein the resolution recovery process includes: transforming the datasets into frequency space; performing a stationary deconvolution on thefrequency space data sets with a filter, the filter used in performingthe stationary deconvolution being$\frac{\sin \left( {n\quad \Delta \quad {\varphi/2}} \right)}{n\quad \Delta \quad {\varphi/2}}{\hat{g}\left( {\omega_{s},\omega_{z},\frac{n}{\omega_{s}}} \right)}$

where Δø is the angular increment over which the data is collected ineach data set, and ĝ(ω_(s),ω_(z)n/ω_(s)) is a filter function forprojection data collected only at the angular increments; andtransforming the stationarily deconvolved data sets from frequency spaceto image space.
 17. The method of claim 16 wherein projection data setswith collected projection data span less than 360°, the resolutionrecovery process function including: zero-filling projection data setsin the angular rotation direction, the zero-filled and actuallycollected projection data sets together spanning 360°; and smoothingeach interface between the actually collected and zero-filled data sets,the smoothed data sets being transformed into frequency space.
 18. Adiagnostic imaging apparatus comprising: at least one detector head fordetecting incident radiation; a collimator mounted to the detector headfor limiting trajectories along which radiation is receivable by thehead; a movable gantry which moves the detector head around a subject inan examination region; a data acquisition system which acquiresprojection data sets from the detector head at angular incrementsspanning less than 360°; a zero-filling processor for generatingzero-filled data sets between the actually collected projection datasets, to create 360° of data sets; a smoothing processor for smoothinginterfaces between the actually collected and zero-filled data sets; aresolution recovery processor for operating on the smoothed data sets; areconstruction processor which reconstructs the resolution recovereddata sets into a three-dimensional image representation; and an imagememory for storing the three-dimensional image representation.
 19. Thediagnostic imaging apparatus as set forth in claim 18 wherein theresolution recovery processor includes: a Fourier transform processorwhich transforms the smoothed data sets into frequency space; and adeconvolution processor which deconvolves the frequency space data setswith a resolution recovering deconvolution function, the deconvolveddata sets being transformed from frequency space back to image space asthe resolution recovered data sets.
 20. The diagnostic imaging apparatusas set forth in claim 19 wherein the gantry moves the detector heads inangular steps, each actually collected data set corresponding to one ofthe angular steps.
 21. The diagnostic imaging apparatus as set forth inclaim 19 wherein the gantry moves the detector heads continuously andthe data acquisition system bins the acquired data into data sets, andthe deconvolution processor deconvolves the data sets with:$\frac{\sin \left( {n\quad \Delta \quad {\varphi/2}} \right)}{n\quad \Delta \quad {\varphi/2}}{\hat{g}\left( {\omega_{s},\omega_{z},\frac{n}{\omega_{s}}} \right)}$

where Δø is the angular increment over which the data is collected ineach data set, and ĝ(ω_(s),ω_(z),n/ω_(s)) is a filter function forprojection data collected only at the angular increments.